%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW535_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:40:24 PM UTC 2026
% Result : Theorem 0.26s 0.38s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-2 aty)
% Number of functors : 38 ( 38 usr; 6 con; 0-5 aty)
% Number of variables : 22 ( 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
huffma1450048681e_tree: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_6,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_7,type,
huffma675207370phabet:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,bool) ) ).
tff(func_def_8,type,
huffma1134658180e_cost:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_9,type,
huffma410068972_depth:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_10,type,
huffma1352802255e_freq:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_11,type,
huffma1146269203erNode:
!>[X0: $tType] : ( ( nat * huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_12,type,
huffma2021818691e_Leaf:
!>[X0: $tType] : ( ( nat * X0 ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_13,type,
huffma107959123e_case:
!>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))) * huffma1450048681e_tree(X0) ) > X1 ) ).
tff(func_def_14,type,
huffma1280178957ee_rec:
!>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))) * huffma1450048681e_tree(X0) ) > X1 ) ).
tff(func_def_15,type,
huffma83463279weight:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_16,type,
inf_inf:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_17,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_18,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_19,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_20,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_21,type,
fFalse: bool ).
tff(func_def_22,type,
fTrue: bool ).
tff(func_def_23,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_24,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_25,type,
t_1: huffma1450048681e_tree(a) ).
tff(func_def_26,type,
t_2: huffma1450048681e_tree(a) ).
tff(func_def_27,type,
w: nat ).
tff(func_def_28,type,
sK0:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_29,type,
sK1:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_30,type,
sK2:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_31,type,
sK3:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_32,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_33,type,
sK5:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_34,type,
sK6:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_35,type,
sK7:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(pred_def_1,type,
bounded_lattice:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
lattice:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
semilattice_inf:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
bounded_lattice_bot:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
huffma1518433673istent:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).
tff(pred_def_18,type,
pp: bool > $o ).
tff(f4,axiom,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(X0,X2),huffma1134658180e_cost(X0,X2)),huffma83463279weight(X0,X1)),huffma1134658180e_cost(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_cost_Osimps_I2_J) ).
tff(f14,axiom,
! [X0: nat,X1: nat,X2: nat] : ( plus_plus(nat,plus_plus(nat,X2,X1),X0) = plus_plus(nat,X2,plus_plus(nat,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_nat__add__assoc) ).
tff(f133,conjecture,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f134,negated_conjecture,
( ( ~ huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) ) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)) ),
inference(negated_conjecture,[status(cth)],[f133]) ).
tff(f136,plain,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)),
inference(flattening,[],[f134]) ).
tff(f206,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(X0,X2),huffma1134658180e_cost(X0,X2)),huffma83463279weight(X0,X1)),huffma1134658180e_cost(X0,X1)) ),
inference(cnf_transformation,[],[f4]) ).
tff(f220,plain,
! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,plus_plus(nat,X2,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
tff(f361,plain,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)),
inference(cnf_transformation,[],[f136]) ).
tff(f424,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,huffma83463279weight(X0,X2),huffma1134658180e_cost(X0,X2)),plus_plus(nat,huffma83463279weight(X0,X1),huffma1134658180e_cost(X0,X1))) ),
inference(forward_demodulation,[],[f206,f220]) ).
tff(f441,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,huffma83463279weight(X0,X2),plus_plus(nat,huffma1134658180e_cost(X0,X2),plus_plus(nat,huffma83463279weight(X0,X1),huffma1134658180e_cost(X0,X1)))) ),
inference(forward_demodulation,[],[f424,f220]) ).
tff(f1077,plain,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),plus_plus(nat,huffma83463279weight(a,t_2),huffma1134658180e_cost(a,t_2))),
inference(superposition,[],[f361,f220]) ).
tff(f1101,plain,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,huffma83463279weight(a,t_1),plus_plus(nat,huffma1134658180e_cost(a,t_1),plus_plus(nat,huffma83463279weight(a,t_2),huffma1134658180e_cost(a,t_2)))),
inference(forward_demodulation,[],[f1077,f220]) ).
tff(f1108,plain,
$false,
inference(forward_subsumption_resolution,[],[f1101,f441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW535_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 % Computer : n003.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8046.5625MB
% 0.09/0.26 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Mon Sep 28 14:19:42 UTC 2026
% 0.09/0.27 % CPUTime :
% 0.09/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.30 Running first-order model finding
% 0.26/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.26/0.38 % (1615225)Will run a generic schedule for satisfiability detection.
% 0.26/0.38 % (1615234)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=523470109:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.26/0.38 % (1615233)dis+10_1_sil=32000:sp=arity:random_seed=3593921532:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.26/0.38 % (1615231)% WARNING: option uhcvi not known.
% 0.26/0.38 % (1615231)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2827059215:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.26/0.38 % (1615230)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1297062397_2999 on theBenchmark for (2999ds/0Mi)
% 0.26/0.38 % (1615232)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=841672938:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.26/0.38 % (1615235)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2645364276:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.26/0.38 % (1615236)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=217010742:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.26/0.38 % Exception at run slice level
% 0.26/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.26/0.38 % (1615234) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1615225-1615234"...
% 0.26/0.38 % (1615234)...printing done.
% 0.26/0.38 % (1615234)Refutation found. Thanks to Tanya!
% 0.26/0.38 % SZS status Theorem for theBenchmark
% 0.26/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.38 % (1615234)------------------------------
% 0.26/0.38 % (1615234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.38 % (1615234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.38 % (1615234)CaDiCaL version: 2.1.3
% 0.26/0.38 % (1615234)Termination reason: Refutation
% 0.26/0.38 % (1615234)Time elapsed: 0.026 s
% 0.26/0.38 % (1615234)Peak memory usage: 12 MB
% 0.26/0.38 % (1615234)Instructions burned: 49 (million)
% 0.26/0.38 % (1615225)Success in time 0.063 s
% 0.26/0.38 % Vampire exiting
%------------------------------------------------------------------------------